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We present a fast and scalable framework, leveraging graph neural networks (GNNs) and hierarchical matrix ($\mathcal{H}$-matrix) techniques, for simulating large-scale particulate suspensions, which have broader impacts across science and…

We propose the GENERIC formalism informed neural networks (GFINNs) that obey the symmetric degeneracy conditions of the GENERIC formalism. GFINNs comprise two modules, each of which contains two components. We model each component using a…

Convolutional Neural Networks (CNNs) have recently led to incredible breakthroughs on a variety of pattern recognition problems. Banks of finite impulse response filters are learned on a hierarchy of layers, each contributing more abstract…

Graph Neural Networks (GNNs) are key tools for graph representation learning, demonstrating strong results across diverse prediction tasks. In this paper, we present Convexified Message-Passing Graph Neural Networks (CGNNs), a novel and…

We introduce Nonlinear GENERIC Informed Neural Networks (N-GINNs), a deep learning framework for discovering evolution equations of systems governed by the nonlinear GENERIC formalism (General Equation for Non-Equilibrium…

The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential…

In this work, we propose a generalized multiscale inversion algorithm for heterogeneous problems that aims at solving an inverse problem on a computational coarse grid. Previous inversion techniques for multiscale problems seek a…

Physics-informed neural networks (PINNs) are a promising approach that combines the power of neural networks with the interpretability of physical modeling. PINNs have shown good practical performance in solving partial differential…

We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In…

A computational approach by an implementation of the Principle Component Analysis (PCA) with K-means and Gaussian Mixture (GM) clustering methods from Machine Learning (ML) algorithms to identify structural and dynamical heterogeneities of…

Graph neural networks (GNNs) have been broadly studied on dynamic graphs for their representation learning, majority of which focus on graphs with homogeneous structures in the spatial domain. However, many real-world graphs - i.e.,…

Preconditioning is at the heart of iterative solutions of large, sparse linear systems of equations in scientific disciplines. Several algebraic approaches, which access no information beyond the matrix itself, are widely studied and used,…

Modeling self-gravitating gas flows is essential to answering many fundamental questions in astrophysics. This spans many topics including planet-forming disks, star-forming clouds, galaxy formation, and the development of large-scale…

3D Gaussian Splatting (3DGS) has made significant strides in real-time 3D scene reconstruction, but faces memory scalability issues in high-resolution scenarios. To address this, we propose Hierarchical Gaussian Splatting (HRGS), a…

Fully unsupervised deep generative modeling (FU-DGM) is promising for compressively sampled MRI (CS-MRI) when training data or compute are limited. Classical FU-DGMs such as DIP and INR rely on architectural priors, but the ill-conditioned…

A recently developed upscaling technique, the multicontinuum homogenization method, has gained significant attention for its effectiveness in modeling complex multiscale systems. This method defines multiple continua based on distinct…

Conventional gradient descent methods compute the gradients for multiple variables through the partial derivative. Treating the coupled variables independently while ignoring the interaction, however, leads to an insufficient optimization…

The rise of Physics-Informed Neural Networks (PINNs) has popularized the concept of solving differential equations via residual minimization. However, neural networks are often viewed as ``black boxes" requiring significant computational…

We combine concepts from multilevel solvers for partial differential equations (PDEs) with neural network based deep learning and propose a new methodology for the efficient numerical solution of high-dimensional parametric PDEs. An…

The field of 3D reconstruction from images has rapidly evolved in the past few years, first with the introduction of Neural Radiance Field (NeRF) and more recently with 3D Gaussian Splatting (3DGS). The latter provides a significant edge…